Elements of natural philosophy (Volume 2-3) . ons, Fom internal — . reflexions: d = 2flT — fl + l.* (102) but in each of the triangles whose bases are the equalchords, and common vertex the centre of the drop, Angle subtended y — ^ — 2 -{n-l)« • • • .(103) Because the chords are all equal, the last angle of in-cidence CB D, within the drop in Fig. (87), or CB D\ Substitution ; ELEMENTS OF OPTICS. 317 in Fig. (88), is equal to the angle of refraction C A D, Angle of emergence eoual and hence the angle of emergence C B m\ is equal to to angle ofthe angle of incidence CAm. incidence; The angle A
Elements of natural philosophy (Volume 2-3) . ons, Fom internal — . reflexions: d = 2flT — fl + l.* (102) but in each of the triangles whose bases are the equalchords, and common vertex the centre of the drop, Angle subtended y — ^ — 2 -{n-l)« • • • .(103) Because the chords are all equal, the last angle of in-cidence CB D, within the drop in Fig. (87), or CB D\ Substitution ; ELEMENTS OF OPTICS. 317 in Fig. (88), is equal to the angle of refraction C A D, Angle of emergence eoual and hence the angle of emergence C B m\ is equal to to angle ofthe angle of incidence CAm. incidence; The angle A 0 B, in Fig. (87), is the supplement of thetotal deviation of the emergent from the incident ray,and is equal to the angle B EF, subtended by the ra- References todius of the bow; in Fig. (88), it is the excess of total de- figures;viation above 180°. Calling this angle 5, we shall have , Notation and equation; S==F{29—6); Fig. Illustration forsecondary bow; the upper sign referring to Fig. (87), and the lower toFig. (88); replacing 0, by its value in Equation (103,) theabove reduces to General value 8 = zri(2(p — 2(n + 1) 9 + ft — 1 . *) . (104)f()r radiua of a colored arch; this, with equation From which the sin 9 = m . sin 9, (105) F radius of anyparticular color will enable us to determine the value of £, when 9 and m ™n bc found;are given for any particular color. For any value of 9, assumed arbitrarily, 8 will, in gen-eral, correspond to rays of the same color so much dif-fused as to produce little or no impression upon the eye;but if 9 be taken such as to give S a maximum or mini- 318 NATURAL PHILOSOPHY what waves mum then will the rays corresponding to ?n. emerge i>a- appcrtain to the ?/ r © o I rainbow. rallel, or nearly so, for a small variation in the angle 9 on either side of that from which this maximum orminimum value of S results; hence, the waves which en-ter the eye in this case
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